TSTP Solution File: REL003+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : REL003+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 19:38:17 EDT 2022
% Result : Theorem 0.19s 0.44s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 24
% Syntax : Number of formulae : 142 ( 131 unt; 10 typ; 0 def)
% Number of atoms : 393 ( 273 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 932 ( 28 ~; 4 |; 9 &; 877 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 217 ( 0 ^ 217 !; 0 ?; 217 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_complement,type,
complement: $i > $i ).
thf(tp_composition,type,
composition: $i > $i > $i ).
thf(tp_converse,type,
converse: $i > $i ).
thf(tp_join,type,
join: $i > $i > $i ).
thf(tp_meet,type,
meet: $i > $i > $i ).
thf(tp_one,type,
one: $i ).
thf(tp_sK1_X0,type,
sK1_X0: $i ).
thf(tp_sK2_SY27,type,
sK2_SY27: $i ).
thf(tp_top,type,
top: $i ).
thf(tp_zero,type,
zero: $i ).
thf(1,axiom,
! [X0: $i] :
( zero
= ( meet @ X0 @ ( complement @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero) ).
thf(2,axiom,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_top) ).
thf(3,axiom,
! [X0: $i,X1: $i] :
( ( join @ ( composition @ ( converse @ X0 ) @ ( complement @ ( composition @ X0 @ X1 ) ) ) @ ( complement @ X1 ) )
= ( complement @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_cancellativity) ).
thf(4,axiom,
! [X0: $i,X1: $i] :
( ( converse @ ( composition @ X0 @ X1 ) )
= ( composition @ ( converse @ X1 ) @ ( converse @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_multiplicativity) ).
thf(5,axiom,
! [X0: $i,X1: $i] :
( ( converse @ ( join @ X0 @ X1 ) )
= ( join @ ( converse @ X0 ) @ ( converse @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity) ).
thf(6,axiom,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence) ).
thf(7,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( composition @ ( join @ X0 @ X1 ) @ X2 )
= ( join @ ( composition @ X0 @ X2 ) @ ( composition @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_distributivity) ).
thf(8,axiom,
! [X0: $i] :
( ( composition @ X0 @ one )
= X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_identity) ).
thf(9,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( composition @ X0 @ ( composition @ X1 @ X2 ) )
= ( composition @ ( composition @ X0 @ X1 ) @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_associativity) ).
thf(10,axiom,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).
thf(11,axiom,
! [X0: $i,X1: $i] :
( X0
= ( join @ ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
thf(12,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X1 @ X2 ) )
= ( join @ ( join @ X0 @ X1 ) @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux2_join_associativity) ).
thf(13,axiom,
! [X0: $i,X1: $i] :
( ( join @ X0 @ X1 )
= ( join @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
thf(14,conjecture,
! [X0: $i,X1: $i] :
( ( ( ( join @ X0 @ X1 )
= X1 )
=> ( ( join @ ( converse @ X0 ) @ ( converse @ X1 ) )
= ( converse @ X1 ) ) )
& ( ( ( join @ ( converse @ X0 ) @ ( converse @ X1 ) )
= ( converse @ X1 ) )
=> ( ( join @ X0 @ X1 )
= X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(15,negated_conjecture,
( ( ! [X0: $i,X1: $i] :
( ( ( ( join @ X0 @ X1 )
= X1 )
=> ( ( join @ ( converse @ X0 ) @ ( converse @ X1 ) )
= ( converse @ X1 ) ) )
& ( ( ( join @ ( converse @ X0 ) @ ( converse @ X1 ) )
= ( converse @ X1 ) )
=> ( ( join @ X0 @ X1 )
= X1 ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[14]) ).
thf(16,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( ( join @ X0 @ X1 )
= X1 )
=> ( ( join @ ( converse @ X0 ) @ ( converse @ X1 ) )
= ( converse @ X1 ) ) )
& ( ( ( join @ ( converse @ X0 ) @ ( converse @ X1 ) )
= ( converse @ X1 ) )
=> ( ( join @ X0 @ X1 )
= X1 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[15]) ).
thf(17,plain,
( ( ! [X0: $i] :
( zero
= ( meet @ X0 @ ( complement @ X0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(18,plain,
( ( ! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(19,plain,
( ( ! [X0: $i,X1: $i] :
( ( join @ ( composition @ ( converse @ X0 ) @ ( complement @ ( composition @ X0 @ X1 ) ) ) @ ( complement @ X1 ) )
= ( complement @ X1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [X0: $i,X1: $i] :
( ( converse @ ( composition @ X0 @ X1 ) )
= ( composition @ ( converse @ X1 ) @ ( converse @ X0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(21,plain,
( ( ! [X0: $i,X1: $i] :
( ( converse @ ( join @ X0 @ X1 ) )
= ( join @ ( converse @ X0 ) @ ( converse @ X1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(22,plain,
( ( ! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(23,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( composition @ ( join @ X0 @ X1 ) @ X2 )
= ( join @ ( composition @ X0 @ X2 ) @ ( composition @ X1 @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(24,plain,
( ( ! [X0: $i] :
( ( composition @ X0 @ one )
= X0 ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(25,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( composition @ X0 @ ( composition @ X1 @ X2 ) )
= ( composition @ ( composition @ X0 @ X1 ) @ X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(26,plain,
( ( ! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(27,plain,
( ( ! [X0: $i,X1: $i] :
( X0
= ( join @ ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(28,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X1 @ X2 ) )
= ( join @ ( join @ X0 @ X1 ) @ X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(29,plain,
( ( ! [X0: $i,X1: $i] :
( ( join @ X0 @ X1 )
= ( join @ X1 @ X0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(30,plain,
( ( ! [SY27: $i] :
( ( ( ( join @ sK1_X0 @ SY27 )
= SY27 )
=> ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ SY27 ) )
= ( converse @ SY27 ) ) )
& ( ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ SY27 ) )
= ( converse @ SY27 ) )
=> ( ( join @ sK1_X0 @ SY27 )
= SY27 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(31,plain,
( ( ( ( ( join @ sK1_X0 @ sK2_SY27 )
= sK2_SY27 )
=> ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY27 ) )
= ( converse @ sK2_SY27 ) ) )
& ( ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY27 ) )
= ( converse @ sK2_SY27 ) )
=> ( ( join @ sK1_X0 @ sK2_SY27 )
= sK2_SY27 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[30]) ).
thf(32,plain,
( ( ( ( join @ sK1_X0 @ sK2_SY27 )
= sK2_SY27 )
=> ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY27 ) )
= ( converse @ sK2_SY27 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[31]) ).
thf(33,plain,
( ( ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY27 ) )
= ( converse @ sK2_SY27 ) )
=> ( ( join @ sK1_X0 @ sK2_SY27 )
= sK2_SY27 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[31]) ).
thf(34,plain,
( ( ~ ( ( ( join @ sK1_X0 @ sK2_SY27 )
= sK2_SY27 )
=> ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY27 ) )
= ( converse @ sK2_SY27 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[32]) ).
thf(35,plain,
( ( ~ ( ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY27 ) )
= ( converse @ sK2_SY27 ) )
=> ( ( join @ sK1_X0 @ sK2_SY27 )
= sK2_SY27 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[33]) ).
thf(36,plain,
( ( ( ( join @ sK1_X0 @ sK2_SY27 )
= sK2_SY27 )
& ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY27 ) )
!= ( converse @ sK2_SY27 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(37,plain,
( ( ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY27 ) )
= ( converse @ sK2_SY27 ) )
& ( ( join @ sK1_X0 @ sK2_SY27 )
!= sK2_SY27 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(38,plain,
( ( ! [X0: $i,X1: $i] :
( ( join @ X0 @ X1 )
= ( join @ X1 @ X0 ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(39,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X1 @ X2 ) )
= ( join @ ( join @ X0 @ X1 ) @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(40,plain,
( ( ! [X0: $i,X1: $i] :
( X0
= ( join @ ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(41,plain,
( ( ! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(42,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( composition @ X0 @ ( composition @ X1 @ X2 ) )
= ( composition @ ( composition @ X0 @ X1 ) @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(43,plain,
( ( ! [X0: $i] :
( ( composition @ X0 @ one )
= X0 ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(44,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( composition @ ( join @ X0 @ X1 ) @ X2 )
= ( join @ ( composition @ X0 @ X2 ) @ ( composition @ X1 @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(45,plain,
( ( ! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(46,plain,
( ( ! [X0: $i,X1: $i] :
( ( converse @ ( join @ X0 @ X1 ) )
= ( join @ ( converse @ X0 ) @ ( converse @ X1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(47,plain,
( ( ! [X0: $i,X1: $i] :
( ( converse @ ( composition @ X0 @ X1 ) )
= ( composition @ ( converse @ X1 ) @ ( converse @ X0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(48,plain,
( ( ! [X0: $i,X1: $i] :
( ( join @ ( composition @ ( converse @ X0 ) @ ( complement @ ( composition @ X0 @ X1 ) ) ) @ ( complement @ X1 ) )
= ( complement @ X1 ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(49,plain,
( ( ! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(50,plain,
( ( ! [X0: $i] :
( zero
= ( meet @ X0 @ ( complement @ X0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(51,plain,
( ( ( ( join @ sK1_X0 @ sK2_SY27 )
= sK2_SY27 )
& ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY27 ) )
!= ( converse @ sK2_SY27 ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(52,plain,
( ( ~ ( ( ( join @ sK1_X0 @ sK2_SY27 )
!= sK2_SY27 )
| ~ ( ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY27 ) )
!= ( converse @ sK2_SY27 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(53,plain,
! [SV1: $i] :
( ( ! [SY28: $i] :
( ( join @ SV1 @ SY28 )
= ( join @ SY28 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(54,plain,
! [SV2: $i] :
( ( ! [SY29: $i,SY30: $i] :
( ( join @ SV2 @ ( join @ SY29 @ SY30 ) )
= ( join @ ( join @ SV2 @ SY29 ) @ SY30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(55,plain,
! [SV3: $i] :
( ( ! [SY31: $i] :
( SV3
= ( join @ ( complement @ ( join @ ( complement @ SV3 ) @ ( complement @ SY31 ) ) ) @ ( complement @ ( join @ ( complement @ SV3 ) @ SY31 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(56,plain,
! [SV4: $i] :
( ( ! [SY32: $i] :
( ( meet @ SV4 @ SY32 )
= ( complement @ ( join @ ( complement @ SV4 ) @ ( complement @ SY32 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(57,plain,
! [SV5: $i] :
( ( ! [SY33: $i,SY34: $i] :
( ( composition @ SV5 @ ( composition @ SY33 @ SY34 ) )
= ( composition @ ( composition @ SV5 @ SY33 ) @ SY34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(58,plain,
! [SV6: $i] :
( ( ( composition @ SV6 @ one )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(59,plain,
! [SV7: $i] :
( ( ! [SY35: $i,SY36: $i] :
( ( composition @ ( join @ SV7 @ SY35 ) @ SY36 )
= ( join @ ( composition @ SV7 @ SY36 ) @ ( composition @ SY35 @ SY36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(60,plain,
! [SV8: $i] :
( ( ( converse @ ( converse @ SV8 ) )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(61,plain,
! [SV9: $i] :
( ( ! [SY37: $i] :
( ( converse @ ( join @ SV9 @ SY37 ) )
= ( join @ ( converse @ SV9 ) @ ( converse @ SY37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(62,plain,
! [SV10: $i] :
( ( ! [SY38: $i] :
( ( converse @ ( composition @ SV10 @ SY38 ) )
= ( composition @ ( converse @ SY38 ) @ ( converse @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(63,plain,
! [SV11: $i] :
( ( ! [SY39: $i] :
( ( join @ ( composition @ ( converse @ SV11 ) @ ( complement @ ( composition @ SV11 @ SY39 ) ) ) @ ( complement @ SY39 ) )
= ( complement @ SY39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(64,plain,
! [SV12: $i] :
( ( top
= ( join @ SV12 @ ( complement @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(65,plain,
! [SV13: $i] :
( ( zero
= ( meet @ SV13 @ ( complement @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(66,plain,
( ( ( ( join @ sK1_X0 @ sK2_SY27 )
!= sK2_SY27 )
| ~ ( ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY27 ) )
!= ( converse @ sK2_SY27 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(67,plain,
! [SV14: $i,SV1: $i] :
( ( ( join @ SV1 @ SV14 )
= ( join @ SV14 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(68,plain,
! [SV15: $i,SV2: $i] :
( ( ! [SY40: $i] :
( ( join @ SV2 @ ( join @ SV15 @ SY40 ) )
= ( join @ ( join @ SV2 @ SV15 ) @ SY40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(69,plain,
! [SV16: $i,SV3: $i] :
( ( SV3
= ( join @ ( complement @ ( join @ ( complement @ SV3 ) @ ( complement @ SV16 ) ) ) @ ( complement @ ( join @ ( complement @ SV3 ) @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(70,plain,
! [SV17: $i,SV4: $i] :
( ( ( meet @ SV4 @ SV17 )
= ( complement @ ( join @ ( complement @ SV4 ) @ ( complement @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(71,plain,
! [SV18: $i,SV5: $i] :
( ( ! [SY41: $i] :
( ( composition @ SV5 @ ( composition @ SV18 @ SY41 ) )
= ( composition @ ( composition @ SV5 @ SV18 ) @ SY41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(72,plain,
! [SV19: $i,SV7: $i] :
( ( ! [SY42: $i] :
( ( composition @ ( join @ SV7 @ SV19 ) @ SY42 )
= ( join @ ( composition @ SV7 @ SY42 ) @ ( composition @ SV19 @ SY42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(73,plain,
! [SV20: $i,SV9: $i] :
( ( ( converse @ ( join @ SV9 @ SV20 ) )
= ( join @ ( converse @ SV9 ) @ ( converse @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(74,plain,
! [SV21: $i,SV10: $i] :
( ( ( converse @ ( composition @ SV10 @ SV21 ) )
= ( composition @ ( converse @ SV21 ) @ ( converse @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(75,plain,
! [SV22: $i,SV11: $i] :
( ( ( join @ ( composition @ ( converse @ SV11 ) @ ( complement @ ( composition @ SV11 @ SV22 ) ) ) @ ( complement @ SV22 ) )
= ( complement @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(76,plain,
( ( ( ( join @ sK1_X0 @ sK2_SY27 )
!= sK2_SY27 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(77,plain,
( ( ~ ( ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY27 ) )
!= ( converse @ sK2_SY27 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(78,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( join @ SV2 @ ( join @ SV15 @ SV23 ) )
= ( join @ ( join @ SV2 @ SV15 ) @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(79,plain,
! [SV24: $i,SV18: $i,SV5: $i] :
( ( ( composition @ SV5 @ ( composition @ SV18 @ SV24 ) )
= ( composition @ ( composition @ SV5 @ SV18 ) @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(80,plain,
! [SV25: $i,SV19: $i,SV7: $i] :
( ( ( composition @ ( join @ SV7 @ SV19 ) @ SV25 )
= ( join @ ( composition @ SV7 @ SV25 ) @ ( composition @ SV19 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(81,plain,
( ( ( join @ sK1_X0 @ sK2_SY27 )
= sK2_SY27 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(82,plain,
( ( ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY27 ) )
!= ( converse @ sK2_SY27 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(83,plain,
( ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY27 ) )
= ( converse @ sK2_SY27 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(84,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[58,83,81,80,79,78,75,74,73,70,69,67,65,64,60]) ).
thf(85,plain,
( ( ! [X0: $i,X1: $i] :
( ( join @ X0 @ X1 )
= ( join @ X1 @ X0 ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(86,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X1 @ X2 ) )
= ( join @ ( join @ X0 @ X1 ) @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(87,plain,
( ( ! [X0: $i,X1: $i] :
( X0
= ( join @ ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(88,plain,
( ( ! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(89,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( composition @ X0 @ ( composition @ X1 @ X2 ) )
= ( composition @ ( composition @ X0 @ X1 ) @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(90,plain,
( ( ! [X0: $i] :
( ( composition @ X0 @ one )
= X0 ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(91,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( composition @ ( join @ X0 @ X1 ) @ X2 )
= ( join @ ( composition @ X0 @ X2 ) @ ( composition @ X1 @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(92,plain,
( ( ! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(93,plain,
( ( ! [X0: $i,X1: $i] :
( ( converse @ ( join @ X0 @ X1 ) )
= ( join @ ( converse @ X0 ) @ ( converse @ X1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(94,plain,
( ( ! [X0: $i,X1: $i] :
( ( converse @ ( composition @ X0 @ X1 ) )
= ( composition @ ( converse @ X1 ) @ ( converse @ X0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(95,plain,
( ( ! [X0: $i,X1: $i] :
( ( join @ ( composition @ ( converse @ X0 ) @ ( complement @ ( composition @ X0 @ X1 ) ) ) @ ( complement @ X1 ) )
= ( complement @ X1 ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(96,plain,
( ( ! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(97,plain,
( ( ! [X0: $i] :
( zero
= ( meet @ X0 @ ( complement @ X0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(98,plain,
( ( ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY27 ) )
= ( converse @ sK2_SY27 ) )
& ( ( join @ sK1_X0 @ sK2_SY27 )
!= sK2_SY27 ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(99,plain,
( ( ~ ( ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY27 ) )
!= ( converse @ sK2_SY27 ) )
| ~ ( ( ( join @ sK1_X0 @ sK2_SY27 )
!= sK2_SY27 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(100,plain,
! [SV26: $i] :
( ( ! [SY43: $i] :
( ( join @ SV26 @ SY43 )
= ( join @ SY43 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(101,plain,
! [SV27: $i] :
( ( ! [SY44: $i,SY45: $i] :
( ( join @ SV27 @ ( join @ SY44 @ SY45 ) )
= ( join @ ( join @ SV27 @ SY44 ) @ SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(102,plain,
! [SV28: $i] :
( ( ! [SY46: $i] :
( SV28
= ( join @ ( complement @ ( join @ ( complement @ SV28 ) @ ( complement @ SY46 ) ) ) @ ( complement @ ( join @ ( complement @ SV28 ) @ SY46 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(103,plain,
! [SV29: $i] :
( ( ! [SY47: $i] :
( ( meet @ SV29 @ SY47 )
= ( complement @ ( join @ ( complement @ SV29 ) @ ( complement @ SY47 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(104,plain,
! [SV30: $i] :
( ( ! [SY48: $i,SY49: $i] :
( ( composition @ SV30 @ ( composition @ SY48 @ SY49 ) )
= ( composition @ ( composition @ SV30 @ SY48 ) @ SY49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(105,plain,
! [SV31: $i] :
( ( ( composition @ SV31 @ one )
= SV31 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(106,plain,
! [SV32: $i] :
( ( ! [SY50: $i,SY51: $i] :
( ( composition @ ( join @ SV32 @ SY50 ) @ SY51 )
= ( join @ ( composition @ SV32 @ SY51 ) @ ( composition @ SY50 @ SY51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(107,plain,
! [SV33: $i] :
( ( ( converse @ ( converse @ SV33 ) )
= SV33 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(108,plain,
! [SV34: $i] :
( ( ! [SY52: $i] :
( ( converse @ ( join @ SV34 @ SY52 ) )
= ( join @ ( converse @ SV34 ) @ ( converse @ SY52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(109,plain,
! [SV35: $i] :
( ( ! [SY53: $i] :
( ( converse @ ( composition @ SV35 @ SY53 ) )
= ( composition @ ( converse @ SY53 ) @ ( converse @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(110,plain,
! [SV36: $i] :
( ( ! [SY54: $i] :
( ( join @ ( composition @ ( converse @ SV36 ) @ ( complement @ ( composition @ SV36 @ SY54 ) ) ) @ ( complement @ SY54 ) )
= ( complement @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(111,plain,
! [SV37: $i] :
( ( top
= ( join @ SV37 @ ( complement @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(112,plain,
! [SV38: $i] :
( ( zero
= ( meet @ SV38 @ ( complement @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(113,plain,
( ( ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY27 ) )
!= ( converse @ sK2_SY27 ) )
| ~ ( ( ( join @ sK1_X0 @ sK2_SY27 )
!= sK2_SY27 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(114,plain,
! [SV39: $i,SV26: $i] :
( ( ( join @ SV26 @ SV39 )
= ( join @ SV39 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(115,plain,
! [SV40: $i,SV27: $i] :
( ( ! [SY55: $i] :
( ( join @ SV27 @ ( join @ SV40 @ SY55 ) )
= ( join @ ( join @ SV27 @ SV40 ) @ SY55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(116,plain,
! [SV41: $i,SV28: $i] :
( ( SV28
= ( join @ ( complement @ ( join @ ( complement @ SV28 ) @ ( complement @ SV41 ) ) ) @ ( complement @ ( join @ ( complement @ SV28 ) @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(117,plain,
! [SV42: $i,SV29: $i] :
( ( ( meet @ SV29 @ SV42 )
= ( complement @ ( join @ ( complement @ SV29 ) @ ( complement @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(118,plain,
! [SV43: $i,SV30: $i] :
( ( ! [SY56: $i] :
( ( composition @ SV30 @ ( composition @ SV43 @ SY56 ) )
= ( composition @ ( composition @ SV30 @ SV43 ) @ SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(119,plain,
! [SV44: $i,SV32: $i] :
( ( ! [SY57: $i] :
( ( composition @ ( join @ SV32 @ SV44 ) @ SY57 )
= ( join @ ( composition @ SV32 @ SY57 ) @ ( composition @ SV44 @ SY57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(120,plain,
! [SV45: $i,SV34: $i] :
( ( ( converse @ ( join @ SV34 @ SV45 ) )
= ( join @ ( converse @ SV34 ) @ ( converse @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(121,plain,
! [SV46: $i,SV35: $i] :
( ( ( converse @ ( composition @ SV35 @ SV46 ) )
= ( composition @ ( converse @ SV46 ) @ ( converse @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(122,plain,
! [SV47: $i,SV36: $i] :
( ( ( join @ ( composition @ ( converse @ SV36 ) @ ( complement @ ( composition @ SV36 @ SV47 ) ) ) @ ( complement @ SV47 ) )
= ( complement @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(123,plain,
( ( ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY27 ) )
!= ( converse @ sK2_SY27 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(124,plain,
( ( ~ ( ( ( join @ sK1_X0 @ sK2_SY27 )
!= sK2_SY27 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(125,plain,
! [SV48: $i,SV40: $i,SV27: $i] :
( ( ( join @ SV27 @ ( join @ SV40 @ SV48 ) )
= ( join @ ( join @ SV27 @ SV40 ) @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(126,plain,
! [SV49: $i,SV43: $i,SV30: $i] :
( ( ( composition @ SV30 @ ( composition @ SV43 @ SV49 ) )
= ( composition @ ( composition @ SV30 @ SV43 ) @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(127,plain,
! [SV50: $i,SV44: $i,SV32: $i] :
( ( ( composition @ ( join @ SV32 @ SV44 ) @ SV50 )
= ( join @ ( composition @ SV32 @ SV50 ) @ ( composition @ SV44 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(128,plain,
( ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY27 ) )
= ( converse @ sK2_SY27 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(129,plain,
( ( ( ( join @ sK1_X0 @ sK2_SY27 )
!= sK2_SY27 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(130,plain,
( ( ( join @ sK1_X0 @ sK2_SY27 )
= sK2_SY27 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(131,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[105,130,128,127,126,125,122,121,120,117,116,114,112,111,107]) ).
thf(132,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[131,84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : REL003+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.33 % Computer : n013.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Fri Jul 8 13:14:59 EDT 2022
% 0.14/0.33 % CPUTime :
% 0.14/0.34
% 0.14/0.34 No.of.Axioms: 13
% 0.14/0.34
% 0.14/0.34 Length.of.Defs: 0
% 0.14/0.34
% 0.14/0.34 Contains.Choice.Funs: false
% 0.14/0.35 (rf:0,axioms:13,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:15,loop_count:0,foatp_calls:0,translation:fof_full)......
% 0.19/0.44
% 0.19/0.44 ********************************
% 0.19/0.44 * All subproblems solved! *
% 0.19/0.44 ********************************
% 0.19/0.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:13,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:131,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.45
% 0.19/0.45 %**** Beginning of derivation protocol ****
% 0.19/0.45 % SZS output start CNFRefutation
% See solution above
% 0.19/0.45
% 0.19/0.45 %**** End of derivation protocol ****
% 0.19/0.45 %**** no. of clauses in derivation: 132 ****
% 0.19/0.45 %**** clause counter: 131 ****
% 0.19/0.45
% 0.19/0.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:13,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:131,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------